4/15 should be your answer!
Answer:
![(A)m\angle 2=125^\circ\\(C)m\angle 8=55^\circ\\(E)m\angle 14=100^\circ](https://tex.z-dn.net/?f=%28A%29m%5Cangle%202%3D125%5E%5Ccirc%5C%5C%28C%29m%5Cangle%208%3D55%5E%5Ccirc%5C%5C%28E%29m%5Cangle%2014%3D100%5E%5Ccirc)
Step-by-step explanation:
The diagram of the problem is drawn and attached.
Given that:
![m\angle 9 =80^\circ\\m\angle 5 =55^\circ](https://tex.z-dn.net/?f=m%5Cangle%209%20%3D80%5E%5Ccirc%5C%5Cm%5Cangle%205%20%3D55%5E%5Ccirc)
![m\angle 5+ m\angle 6=180^\circ\\55^\circ+ m\angle 6=180^\circ\\m\angle 6=180^\circ-55^\circ\\m\angle 6=125^\circ\\$Now:\\m\angle 6 = m\angle 2 $(Corresponging angles)\\Therefore m\angle 2=125^\circ\\](https://tex.z-dn.net/?f=m%5Cangle%205%2B%20m%5Cangle%206%3D180%5E%5Ccirc%5C%5C55%5E%5Ccirc%2B%20m%5Cangle%206%3D180%5E%5Ccirc%5C%5Cm%5Cangle%206%3D180%5E%5Ccirc-55%5E%5Ccirc%5C%5Cm%5Cangle%206%3D125%5E%5Ccirc%5C%5C%24Now%3A%5C%5Cm%5Cangle%206%20%3D%20m%5Cangle%202%20%24%28Corresponging%20angles%29%5C%5CTherefore%20m%5Cangle%202%3D125%5E%5Ccirc%5C%5C)
![m\angle 5= m\angle 8=55^\circ $(Vertically Opposite Angles)](https://tex.z-dn.net/?f=m%5Cangle%205%3D%20m%5Cangle%208%3D55%5E%5Ccirc%20%24%28Vertically%20Opposite%20Angles%29)
Also
![m\angle 9+ m\angle 10=180^\circ\\80^\circ+ m\angle 10=180^\circ\\m\angle 10=180^\circ-80^\circ\\m\angle 10=100^\circ\\$Now:\\m\angle 10 = m\angle 14 $(Corresponging angles)\\Therefore m\angle 14=100^\circ\\](https://tex.z-dn.net/?f=m%5Cangle%209%2B%20m%5Cangle%2010%3D180%5E%5Ccirc%5C%5C80%5E%5Ccirc%2B%20m%5Cangle%2010%3D180%5E%5Ccirc%5C%5Cm%5Cangle%2010%3D180%5E%5Ccirc-80%5E%5Ccirc%5C%5Cm%5Cangle%2010%3D100%5E%5Ccirc%5C%5C%24Now%3A%5C%5Cm%5Cangle%2010%20%3D%20m%5Cangle%2014%20%24%28Corresponging%20angles%29%5C%5CTherefore%20m%5Cangle%2014%3D100%5E%5Ccirc%5C%5C)
If you call x the total value of the sales, the sale over 12,000 will be: g(x) = 12,000 - x.
And the commission is 4.1% of that = 0.041 * (12,000 - x) = 0.041 * g(x)
So, if f(x) = 0.041x, to calculate the commission you first have to calculate g(x) = 12,000 - x, and the f(g(x))=0.041[12,000 - x].
Which leads you to the solution for the commission as [f o g] (x) = f (g(x)) = 0.041 (12,000 - x).
Answer: [ f o g] (x)
I = Prt
I=1020
r=0.12 (12% converted to decimal by dividing by 100)
t=5
1020=P(0.12)(5)
1020=P(0.6)
P=1700